Abstract

Square root photocurrent dependences of nanowires on light intensity were reported in the literature without clarification of the limiting effect. In this Letter, we derived a relation excellently fitting the observed nonlinearities and, intensifying the significance of the result, we demonstrated that the fit parameters involved can be employed to determine the impurity concentration and electronic response time of nano-sized semiconductors.

© 2013 Optical Society of America

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References

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  1. C. Bouchenaki, B. Ullrich, J. P. Zielinger, H. N. Cong, and P. Chartier, J. Opt. Soc. Am. B 8, 691 (1991).
    [CrossRef]
  2. K. P. Acharya and B. Ullrich, Proc. SPIE 6890, 68900Q (2008).
    [CrossRef]
  3. T. S. Moss, Photoconductivity in the Elements (Academic, 1952).
  4. T. S. Moss, Optical Properties of Semi-Conductors (Academic, 1959).
  5. R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).
  6. H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).
  7. Space-charge limited photocurrent scales with Iin3/4; see V. D. Mihailetchi, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett.94, 126602 (2005), and references therein.
    [CrossRef]
  8. H. Pick, Ann. Phys. 438, 255 (1948).
    [CrossRef]
  9. It was shown in Ref. [3] that Eq. (1) holds for n- and p-type semiconductors (in the original work called excess conductor and defect conductor); i.e., M refers to the density of either ionized donors or acceptors.
  10. R. N. Hall, Proc. IEE—Part B 106, 923 (1959).
  11. The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.
  12. When the IPC data are plotted versus the incident laser power, as in Fig. 3, the slope parameter σ becomes α/(AhνinBM2) with the unit 1/W. The symbol A stands for the area of the laser spot.
  13. In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
    [CrossRef]
  14. M. D. Tabak and P. J. Warter, Phys. Rev. 148, 982 (1966).
    [CrossRef]
  15. B. Ullrich and H. Xi, Opt. Lett. 35, 3910 (2010).
    [CrossRef]
  16. M. Bleicher, Halbleiter-Optoelektronik (Huethig, 1985).
  17. Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

2011 (2)

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

2010 (1)

2008 (1)

K. P. Acharya and B. Ullrich, Proc. SPIE 6890, 68900Q (2008).
[CrossRef]

2002 (1)

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

1991 (1)

1966 (1)

M. D. Tabak and P. J. Warter, Phys. Rev. 148, 982 (1966).
[CrossRef]

1959 (1)

R. N. Hall, Proc. IEE—Part B 106, 923 (1959).

1948 (1)

H. Pick, Ann. Phys. 438, 255 (1948).
[CrossRef]

Acharya, K. P.

K. P. Acharya and B. Ullrich, Proc. SPIE 6890, 68900Q (2008).
[CrossRef]

Bleicher, M.

M. Bleicher, Halbleiter-Optoelektronik (Huethig, 1985).

Blom, P. W. M.

Space-charge limited photocurrent scales with Iin3/4; see V. D. Mihailetchi, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett.94, 126602 (2005), and references therein.
[CrossRef]

Bouchenaki, C.

Chartier, P.

Cong, H. N.

Graham, R.

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

Hall, R. N.

R. N. Hall, Proc. IEE—Part B 106, 923 (1959).

Khan, M. S.

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

Khan, Z. R.

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

Kim, J.-J.

In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
[CrossRef]

Kim, S. S.

In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
[CrossRef]

Kind, H.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Law, M.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Lee, J.-O.

In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
[CrossRef]

Li, J.

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

Messer, B.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Mihailetchi, V. D.

Space-charge limited photocurrent scales with Iin3/4; see V. D. Mihailetchi, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett.94, 126602 (2005), and references therein.
[CrossRef]

Miller, C.

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

Moss, T. S.

T. S. Moss, Photoconductivity in the Elements (Academic, 1952).

T. S. Moss, Optical Properties of Semi-Conductors (Academic, 1959).

Oh, E.

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

Oh, H.

In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
[CrossRef]

Pick, H.

H. Pick, Ann. Phys. 438, 255 (1948).
[CrossRef]

Tabak, M. D.

M. D. Tabak and P. J. Warter, Phys. Rev. 148, 982 (1966).
[CrossRef]

Ullrich, B.

Warter, P. J.

M. D. Tabak and P. J. Warter, Phys. Rev. 148, 982 (1966).
[CrossRef]

Wildeman, J.

Space-charge limited photocurrent scales with Iin3/4; see V. D. Mihailetchi, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett.94, 126602 (2005), and references therein.
[CrossRef]

Wu, H.

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

Xi, H.

Yan, H.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Yang, P.

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Yang, Y.

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

Yu, D.

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

Zielinger, J. P.

Zulfequar, M.

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

Adv. Mat. (1)

H. Kind, H. Yan, B. Messer, M. Law, and P. Yang, Adv. Mat. 14, 158 (2002).

Ann. Phys. (1)

H. Pick, Ann. Phys. 438, 255 (1948).
[CrossRef]

J. Opt. Soc. Am. B (1)

Mat. Sci. Appl. (1)

Z. R. Khan, M. S. Khan, M. Zulfequar, and M. S. Khan, Mat. Sci. Appl. 2, 340 (2011).

Nano Lett. (1)

R. Graham, C. Miller, E. Oh, and D. Yu, Nano Lett., 11, 717 (2011).

Opt. Lett. (1)

Phys. Rev. (1)

M. D. Tabak and P. J. Warter, Phys. Rev. 148, 982 (1966).
[CrossRef]

Proc. IEE—Part B (1)

R. N. Hall, Proc. IEE—Part B 106, 923 (1959).

Proc. SPIE (1)

K. P. Acharya and B. Ullrich, Proc. SPIE 6890, 68900Q (2008).
[CrossRef]

Other (8)

T. S. Moss, Photoconductivity in the Elements (Academic, 1952).

T. S. Moss, Optical Properties of Semi-Conductors (Academic, 1959).

It was shown in Ref. [3] that Eq. (1) holds for n- and p-type semiconductors (in the original work called excess conductor and defect conductor); i.e., M refers to the density of either ionized donors or acceptors.

Space-charge limited photocurrent scales with Iin3/4; see V. D. Mihailetchi, J. Wildeman, and P. W. M. Blom, Phys. Rev. Lett.94, 126602 (2005), and references therein.
[CrossRef]

The PbS nanowires referred to in this work are not greatly influenced by surface trap states; see Ref. [5], and the follow-up work by Y. Yang, J. Li, H. Wu, E. Oh, and D. Yu, Nano Lett.12, 5890 (2012). Therefore, the M value found is a fair measure of the impurity concentration.

When the IPC data are plotted versus the incident laser power, as in Fig. 3, the slope parameter σ becomes α/(AhνinBM2) with the unit 1/W. The symbol A stands for the area of the laser spot.

In Ref. [6] no information was provided about the impurity concentration in the sample. We noticed, however, that the reported M∼6×1017  cm−3 for ZnO nanowires by H. Oh, J.-J. Kim, J.-O. Lee, and S. S. Kim, J. Korean Phys. Soc.58, 291 (2011), is in good agreement with our fit result. We stress, however, that we do not have specifics about the presence of surface traps in the samples used in Ref. [6], and, therefore, the actual M number can differ from our finding.
[CrossRef]

M. Bleicher, Halbleiter-Optoelektronik (Huethig, 1985).

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Figures (3)

Fig. 1.
Fig. 1.

Linear photocurrent increase versus monochromatic light intensity at 488 nm of thin-film CdS at 300 K.

Fig. 2.
Fig. 2.

Photocurrent of a PbS nanowire versus the intensity of a laser emitting at 532 nm at 300 K (retrieved from Ref. [5]). As indicated, below 200W/cm2 the signal increased linearly, while for elevated intensities a square root dependence was observed (c is a proportionality constant). The broken line (a) represents a power law fit and the solid line (b) was fitted with Eq. (6).

Fig. 3.
Fig. 3.

Photocurrent of a ZnO nanowire versus the power of a laser emitting at 355 nm at 300 K (retrieved from Ref. [6]). The photocurrent behavior is similar to that in Fig. 2. The dotted line (a) represents the power law fit displayed in Ref. [6], while the solid line (b) was fitted with Eq. (6).

Tables (1)

Tables Icon

Table 1. Parameters Used and Calculated B Valuesa

Equations (7)

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G=Bn(n+M),
IPCIin.
IPC(Iin)0.5.
n/M=(1/2)×[{1+4G/(BM2)}(0.5)1].
σ=α/(hνinBM2),
IPC=C[{1+4σIin}(0.5)1],
B=0.58×1012ni(m0/[me+mh])3/2(1+m0/me+m0/mh)Eg2,

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